MAGNETISM AND MATTER
1. INTRODUCTION
This topic deals with the magnetism and the matter. Basically, there are three mainly known matter surrounding us -Solid, Liquid and Gaseous. And two more not mainly known matters - Plasma state and Bohr's Einstein Condensate. Magnetic phenomena are universal in nature. Vast, distant galaxies, the tiny invisible atoms, humans and beasts all are permeated through and through with a host of magnetic fields from a variety of sources. The earth’s magnetism predates human evolution. The word magnet is derived from the name of an island in Greece called magnesia where magnetic ore deposits were found, as early as 600 BC. Shepherds on this island complained that their wooden shoes (which had nails) at times stayed struck to the ground. Their iron-tipped rods were similarly affected. This attractive property of magnets made it difficult for them to move around. The directional property of magnets was also known since ancient times. A thin long piece of a magnet, when suspended freely, pointed in the north-south direction. A similar effect was observed when it was placed on a piece of cork which was then allowed to float in still water. The name lodestone (or loadstone) given to a naturally occurring ore of iron- magnetite means leading stone. The technological exploitation of this property is generally credited to the Chinese. Chinese texts dating 400 BC mention the use of magnetic needles for navigation on ships. Caravans crossing the Gobi desert also employed magnetic needles. A Chinese legend narrates the tale of the victory of the emperor Huang-t i about four thousand years ago, which he owed to his craftsmen (whom nowadays you would call engineers). These ‘engineers’ built a chariot on which they placed a magnetic figure with arms outstretched. The swiveled around so that the finger of the statuette on it always pointed south. With this chariot, Huang-ti’s troops were able to attack the enemy from the rear in thick fog, and to defeat them.
The charges or electric currents produce magnetic fields. This discovery, which was made in the early part of the nineteenth century is credited to Oersted, Ampere, Bio t and S a v art, among others. In the present chapter, we take a look at magnetism as a subject in its own right. Some of the commonly known ideas regarding magnetism are:
(i) Magnets are having two poles namely - North pole and South Pole . In the free state the North Pole of the magnet points towards the North and the South Pole points towards the South.
(i i) The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south to the north.
(i i i) When a bar magnet is freely suspended, it points in the north-south direction. The tip which points to the geographic north is called the north pole and the tip which points to the geographic south is called the south pole of the magnet.
(i v) There is a repulsive force when north poles ( or south poles ) of two magnets are brought close together. Conversely, there is an attractive force between the north pole of one magnet and the south pole of the other.
(v) We cannot isolate the north, or south pole of a magnet. If a bar magnet is broken into two halves, we get two similar bar magnets with somewhat weaker properties. Unlike electric charges, isolated magnetic north and south poles known as magnetic monopoles do not exist.
(v i) It is possible to make magnets out of iron and its alloys.
We begin with a description of a bar magnet and its behaviour in an external magnetic field. We describe Gauss’s law of magnetism. We then follow it up with an account of the earth’s magnetic field. We next describe how materials can be classified on the basis of their magnetic properties. We describe para-, d i a-, and ferromagnetism. We conclude with a section on electromagnets and permanent magnets
2. BAR MAGNET
(i i i) The larger the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B.
(i v) The magnetic field lines do not intersect, for if they did, the direction of the magnetic field would not be unique at the point of intersection.
One can plot the magnetic field lines in a variety of ways. One way is to place a small magnetic compass needle at various positions and note its orientation. This gives us an idea of the magnetic field direction at various points in space.
3. MAGNETISM AND GAUSS’S LAW
We see that for a closed surface represented by i , the number of lines leaving the surface is equal to the number of lines entering it. This is consistent with the fact that no net charge is enclosed by the surface. However, for the closed surface, there is a net outward flux, since it does include a net (positive) charge.
The situation is radically different for magnetic fields which are continuous and form closed loops. Examine the both cases visually demonstrate that the number of magnetic field lines leaving the surface is balanced by the number of lines entering it. The net magnetic flux is zero for both the surfaces. This is true for any closed surface.
Consider a small vector area element ∆S of a closed surface S . The magnetic flux through Ä S is defined as ∆φ B = B.∆S, where B is the field at ∆S. We divide S into many small area elements and calculate the individual flux through each. Then, the net flux φ B is, φ φ B B all all = = = ∑ ∑ ∆ ∆ ’ ’ ’ ’ B. S 0 where ‘all’ stands for ‘all area elements ∆S′. Compare this with the Gauss’s law of electrostatics. The flux through a closed surface in that case is given by
∑ E S .∆ = q ε 0
where q is the electric charge enclosed by the surface. The difference between the Gauss’s law of magnetism and that for electrostatics is a reflection of the fact that isolated magnetic poles (also called monopoles) are not known to exist. There are no sources or sinks of B; the simplest magnetic element is a dipole or a current loop. All magnetic phenomena can be explained in terms of an arrangement of dipoles and/or current loops. Thus, Gauss’s law for magnetism is:
The net magnetic flux through any closed surface is zero.
4. THE EARTH’S MAGNETISM
Earlier we have referred to the magnetic field of the earth. The strength of the earth’s magnetic field varies from place to place on the earth’s surface; its value being of the order of 10–5 T. What causes the earth to have a magnetic field is not clear. Originally the magnetic field was thought of as arising from a giant bar magnet placed approximately along the axis of rotation of the earth and deep in the interior. However, this simplistic picture is certainly not correct. The magnetic field is now thought to arise due to electrical currents produced by convective motion of metallic fluids (consisting mostly of molten iron and nickel) in the outer core of the earth. This is known as the dynamo effect. The magnetic field lines of the earth resemble that of a (hypothetical) magnetic dipole located at the centre of the earth. The axis of the dipole does not coincide with the axis of rotation of the earth but is presently titled by approximately 11.3° with respect to the later. In this way of looking at it, the magnetic poles are located where the magnetic field lines due to the dipole enter or leave the earth. The location of the north magnetic pole is at a latitude of 79.74° N and a longitude of 71.8° W, a place somewhere in north Canada. The magnetic south pole is at 79.74° S, 108.22° E in the Antarctica. The pole near the geographic north pole of the earth is called the north magnetic pole. Likewise, the pole near the geographic south pole is called the south magnetic pole. There is some confusion in the nomenclature of the poles. If one looks at the magnetic field lines of the earth , one sees that unlike in the case of a bar magnet, the field lines go into the earth at the north magnetic pole (Nm ) and come out from the south magnetic pole (S m ). The convention arose because the magnetic north was the direction to which the north pole of a magnetic needle pointed; the north pole of a magnet was so named as it was the north seeking pole. Thus, in reality, the north magnetic pole behaves like the south pole of a bar magnet inside the earth and vice versa.
1. Magnetic declination and dip
Consider a point on the earth’s surface. At such a point, the direction of the longitude circle determines the geographic north-south direction, the line of longitude towards the north pole being the direction of true north. The vertical plane containing the longitude circle and the axis of rotation of the earth is called the geographic meridian. In a similar way, one can define magnetic meridian of a place as the vertical plane which passes through the imaginary line joining the magnetic north and the south poles. This plane would intersect the surface of the earth in a longitude like circle. A magnetic needle, which is free to swing horizontally, would then lie in the magnetic meridian and the north pole of the needle would point towards the magnetic north pole. Since the line joining the magnetic poles is titled with respect to the geographic axis of the earth, the magnetic meridian at a point makes angle with the geographic meridian. This, then, is the angle between the true geographic north and the north shown by a compass needle. This angle is called the magnetic declination or simply declination. The declination is greater at higher latitudes and smaller near the equator. The declination in India is small, it being 0°41′ E at Delhi and 0°58′ W at Mumbai. Thus, at both these places a magnetic needle shows the true north quite accurately. There is one more quantity of interest. If a magnetic needle is perfectly balanced about a horizontal axis so that it can swing in a plane of the magnetic meridian, the needle would make an angle with the horizontal. This is known as the angle of dip (also known as inclination). Thus, dip is the angle that the total magnetic field BE of the earth makes with the surface of the earth. The plane is a section through the earth. The total magnetic field at P can be resolved into a horizontal component HE and a vertical component Z E .
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